Python for Finance: Analyze Big Financial Data

option = call_option(self.S0, self.K, self.T, self.r, sigma_est)
for i in range(it):
option.sigma -= (option.value() - C0) / option.vega()
return option.sigma

This class can be used in an interactive IPython session as follows:

In  [ 1 ]:  from bsm_option_class import call_option

In  [ 2 ]:  o   =   call_option(100.,   105.,   1.0,    0.05,   0.2)

type(o)

Out[2]: bsm_option_class.call_option

In  [ 3 ]:  value   =   o.value()

value

Out[3]: 8.0213522351431763

In  [ 4 ]:  o.vega()

Out[4]: 54.222833358480528

In  [ 5 ]:  o.imp_vol(C0=value)

Out[5]: 0.20000000000000001

The option class can be easily used to visualize, for example, the value and Vega of the

option for different strikes and maturities. This is, in the end, one of the major advantages

of having such formulae available. The following Python code generates the option

statistics for different maturity-strike combinations:

In  [ 6 ]:  import numpy as np

maturities  =   np.linspace(0.05,   2.0,     20 )

strikes =   np.linspace( 80 ,    120 ,   20 )

T,  K   =   np.meshgrid(strikes,    maturities)

C   =   np.zeros_like(K)

V   =   np.zeros_like(C)

for t in enumerate(maturities):

for k in enumerate(strikes):

o.T =   t[ 1 ]

o.K =   k[ 1 ]

C[t[ 0 ],   k[ 0 ]] =   o.value()

V[t[ 0 ],   k[ 0 ]] =   o.vega()

First, let us have a look at the option values. For plotting, we need to import some libraries

and functions:

In  [ 7 ]:  import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

from pylab import cm

                                %matplotlib inline

The output of the following code is presented in Figure B-1:

In  [ 8 ]:  fig =   plt.figure(figsize=( 12 ,    7 ))

ax  =   fig.gca(projection=‘3d’)

surf    =   ax.plot_surface(T,  K,  C,  rstride= 1 ,    cstride= 1 ,

cmap=cm.coolwarm,   linewidth=0.5,  antialiased=True)

ax.set_xlabel(‘strike’)

ax.set_ylabel(‘maturity’)

ax.set_zlabel(‘European call    option  value’)

fig.colorbar(surf,  shrink=0.5, aspect= 5 )

Second, we have the results for the Vega of the call option, as shown in Figure B-2:

In  [ 9 ]:  fig =   plt.figure(figsize=( 12 ,    7 ))

ax  =   fig.gca(projection=‘3d’)

surf    =   ax.plot_surface(T,  K,  V,  rstride= 1 ,    cstride= 1 ,

cmap=cm.coolwarm,   linewidth=0.5,  antialiased=True)

ax.set_xlabel(‘strike’)

ax.set_ylabel(‘maturity’)

ax.set_zlabel(‘Vega of  European    call    option’)

fig.colorbar(surf,  shrink=0.5, aspect= 5 )

plt.show()